2022 Fiscal Year Final Research Report
Real analysis via sparse domination
| Project/Area Number |
19K03538
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Kyoto University (2020-2022)
Shinshu University (2019) |
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Principal Investigator |
Tsutsui Yohei 京都大学, 理学研究科, 准教授 (40722773)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | Sparse domionation / median / rearrangement / Navier-Stokes 方程式 |
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| Outline of Final Research Achievements |
I explain three results which had been gotten during this project. First, I gave a sparse domination for an integral operator involving the half wave operator. The operator dominates the maximal Riesz operator. The second result is a characterization of the set of medians in terms of rearrangements, and boundedness of fractional maximal operator defined by medians or rearrangements. The last one is a local existence of solutions to the incompressible Navier-Stoes equation with external force and smooth but large initial data.
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| Free Research Field |
実解析学, 偏微分方程式
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| Academic Significance and Societal Importance of the Research Achievements |
2つ目の結果の medain 全体の特徴付けは, medain と rearrangement の関連を明確にできた点は基本的なよい考察であったと考えられる. Median を用いた作用素の有界性については, 今後の Sobolev の不等式に関する研究の出発点となるものである. 最後の Navier-Stokes の局所解の存在については, 近年の流体の方程式の解の非存在や非一意性の研究と対をなすものとなっている.
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